Learn English – Meaning of “sex on the legs”

Well, I bit the bullet and asked the guy what the heck he meant (imagine that). Turns out he was referring to the oft-quoted teach a man to fish proverb.

He also clarified that this is not a common expression, just an idiosyncratic reference he invented and uttered spontaneously.

To add to @Robusto's answer - regarding the origin - the following seems more definitive and is taken from "The Facts on File dictionary of clichés"

To be extremely tired or about to collapse; near the end. Despite the implication, this term never meant that legs were in any way serial—that is, beginning with the first and ending with the last. Rather, it uses last meaning “near the end” (of one’s energy or life). The expression was already used in the sixteenth century; it appears in the play The Old Law (1599) by Thomas Middleton and Philip Massinger: “My husband goes upon his last hour now—on his last legs, I am sure.” In John Ray’s Proverbs (1678) the term is defined as meaning “bankrupt,” and since then it has been transferred to anything nearing its end or about to fail, as in, “This cliché may be on its last legs.”

However this link dates "The Old Law" as

On his last legs. The Old Law (1618-19), Act v. Sc. 1.

The exact text as it appears online

EUGENIA My husband goes upon his last hour now.

FIRST COURTIER On his last legs, I'm sure.

EUGENIA September the seventeenth, I will not bate an hour on it; and tomorrow His latest hour's expired.